LongestPalindromicFactor

The length of the longest factor that reads the same backwards.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001416via BinaryWord✓↗

LongestPalindromicFactor(word)The length of the longest factor that reads the same backwards.

Typed signatures

Type	Package	Applies
(binary_word) -> number	combinatorics	always

Domain: Binary word statistics

Details

• Defined over BinaryWord as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a BinaryWord and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• FindStat's St001416.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 1 else Max(Map(Function(l * Max(Map(
                                                       Function(1 if Max(Sum(Map(
                                                                                  Function((_x[i +
                                                                                               (m - 1)] +
                                                                                            1) *
                                                                                           3 ^
                                                                                           (l - m), m),
                                                                                  Range(1, l, 1),
                                                                                )), 0) ==
                                                                     Max(Sum(Map(
                                                                                  Function((_x[i +
                                                                                               (m - 1)] +
                                                                                            1) *
                                                                                           3 ^
                                                                                           (m - 1), m),
                                                                                  Range(1, l, 1),
                                                                                )), 0) else 0, i),
                                                       Range(1, Length(_x) - l +
                                                                1, 1),
                                                     )), l), Range(1, Length(_x))))

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{LongestPalindromicFactor}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$4$

Properties #

FindStat's value for 0

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0]), \text{LongestPalindromicFactor})$Out$1$

Known value · FindStat St001416

FindStat's value for 1

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([1]), \text{LongestPalindromicFactor})$Out$1$

Known value · FindStat St001416

FindStat's value for 00

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0, 0]), \text{LongestPalindromicFactor})$Out$2$

Known value · FindStat St001416

About

Examples	4
Crosswalk	FindStat